Chebyshev networks learn power oscillations: baking initial speed into the trial solution cuts rotor-angle error from 1.59% to 0.29%
Synopsis
In power-system dynamic simulation, physics-informed neural networks built on multilayer perceptrons are limited by spectral bias toward smooth functions and struggle to capture electromechanical oscillations, while B-spline physics-informed Kolmogorov-Arnold networks are costly to train. mac-PIKAN embeds the closed-form modal response of the linearized swing equation as a fixed term in the trial solution and uses a Chebyshev-basis KAN to learn a nonlinear correction that vanishes at the initial time, so both initial rotor angle and speed hold exactly. On the single-machine infinite-bus benchmark its mean rotor-angle and frequency errors are 0.29% and 0.99%, against 1.59% and 5.26% for the PINN, and the advantage persists with less training data and at lower damping.
Interpretation
Power-system dynamic simulation no longer has to rely on a multilayer perceptron alone to fit rotor-angle trajectories; the network learns only the nonlinear deviation from the modal response of the linearized swing equation. Standard physics-informed neural networks use multilayer perceptrons whose spectral bias toward smooth functions limits their capture of electromechanical oscillations; earlier B-spline physics-informed Kolmogorov-Arnold networks improved accuracy but carried substantial training cost. On the single-machine infinite-bus benchmark, mac-PIKAN reaches mean rotor-angle and frequency errors of 0.29% and 0.99% versus 1.59% and 5.26% for the PINN, and it beats the PINN on all five random seeds, with its worst-seed error of 0.39% still below the PINN mean.
The closed-form modal response from small-signal analysis is precomputed and held fixed, and the network supplies only a nonlinear correction weighted by a quadratic time factor. That correction and its first time derivative vanish at the initial time, so the trial solution satisfies the initial rotor angle and initial speed exactly, whereas a plain c-PIKAN constrains only the initial angle through training data and lets the initial speed drift. Training uses the single-machine infinite-bus benchmark with the original random seed to generate identical training data and collocation points, and errors are evaluated against the reference solution at 100 parameter values and 201 time points, averaged over five random initializations.
Perspective
The demonstrated scope is rotor-angle and frequency prediction on the single-machine infinite-bus benchmark, with training data and collocation points generated under the original benchmark settings and errors evaluated against the reference solution on a test grid of 100 parameter values and 201 time points.
Both methods degrade at lower damping, and at damping 0.11 mac-PIKAN is better on only four of five seeds; mac-PIKAN trains about 8 times slower than the PINN, and validation covers only the single-machine infinite-bus system.